2. BUILDING A MODEL

To build a model of large-scale structure, four key ingredients need
to be specified: (i) the content of Universe, (ii) the initial
conditions, (iii) the growth mechanism, and (iv) the values of
fundamental cosmological parameters. I now discuss each of these in turn.

Densities are usually expressed in terms of the cosmological density
parameter, =
/
crit,
where the critical density,
crit,
is the value that makes the geometry of the Universe
flat. The main constituents of the Universe and their contribution to
are listed in
Table 1.

Table 1. The content of the universe

Component

Contribution to

CMB radiation

r
= 4.7 × 10-5

massless neutrinos

=
3 × 10-5

massive neutrinos

= 6 × 10-2((
< m > ) /
(1 ev))

baryons

b
= 0.037 ± 0.009

(of which stars)

s
= (0.0023 - 0.0041) ± 0.0004

dark matter

dm 0.3

dark energy

0.7

The main contribution to the extragalactic radiation field today is
the cosmic microwave background (CMB), the redshifted radiation left
over from the Big Bang. These photons have been propagating freely
since the epoch of "recombination", approximately 300,000 years after
the Big Bang. The CMB provides a direct observational window to the
conditions that prevailed in the early Universe. The Big Bang also
produced neutrinos which today have an abundance comparable to that of
photons. We do not yet know for certain what, if any, is the mass of
the neutrino, but even for the largest masses that seem plausible at
present, ~ 0.1eV, neutrinos make a negligible contribution to the
total mass budget (although they could be as important as
baryons). The abundance of baryons is now known with reasonable
precision from comparing the abundance of deuterium predicted by Big
Bang theory with observations of the absorption lines produced by
intergalactic gas clouds at high redshift seen along the line-of-sight
to quasars
(Tytler et al. 2000).
Baryons, the overwhelming majority
of which are not in stars today, are also dynamically
unimportant (except, perhaps, in the cores of galaxies).

Dark matter makes up most of the matter content of the Universe today. To
the now firm dynamical evidence for its existence in galaxy halos, even
more direct evidence has been added by the phenomenon of gravitational
lensing which has now been detected around galaxy halos (e.g.
Fischer et al. 2000,
McKay et al. 2001,
Wilson et al. 2001),
in galaxy clusters (e.g.
Clowe et al. 2000),
and in the general mass field (e.g.
Van Waerbeke et al. 2001
and references therein). The distribution of dark matter in rich clusters
can be reconstructed in fair detail from the weak lensing of distant
background galaxies in what amounts virtually to imaging the cluster dark
matter. Various dynamical tests are converging on a value of
dm 0.3, which is also
consistent with independent determinations
such as those based on the baryon fraction in clusters
(White et al. 1993,
Evrard 1997),
and on the evolution in the abundance of galaxy clusters
(Eke et al. 1998,
Borgani et al. 2001).
Since
dm is
much larger than
b, it
follows that the dark matter cannot be made of baryons. The
most popular candidate for the dark matter is a hypothetical elementary
particle like those predicted by supersymmetric theories of particle
physics. These particles are referred to generically as cold dark matter or
CDM. (Hot dark matter is also possible, for example, if the neutrino had a
mass of ~ 5 eV. However, early cosmological simulations showed that the
galaxy distribution in a universe dominated by hot dark matter would not
resemble that observed in our Universe
(White, Frenk and Davis
1983).)

A recent addition to the cosmic budget is the dark energy, direct evidence
for which was first provided by studies of type Ia supernovae
(Riess et al. 1998,
Perlmutter et al. 1999)
(2).
These presumed `standard candles' can now be observed at redshifts
between 0.5 and 1 and beyond. The more distant ones are fainter than would
be expected if the universal expansion were decelerating today, indicating
that the expansion is, in fact, accelerating. Within the standard Friedmann
cosmology, there is only one agent that can produce an accelerating
expansion. This is nowadays known as dark energy, a generalization of the
cosmological constant first introduced by Einstein, which could, in
principle, vary with time. The supernova evidence is consistent with the
value 0.7. Further,
independent evidence for dark
energy is provided by a recent joint analysis of CMB data (see next
section) and the 2dFGRS
(Efstathiou et al. 2002).

Amazingly, when all the components are added together, the data are
consistent with a flat universe:

(2.1)

2 The possibility that dark energy
might be the dynamically dominant component had been anticipated by
theorists from studies of the cosmic large-scale structure (see e.g.
Efstathiou et al. 1990),
and was considered in the first simulations of
structure formation in cold dark matter universes
(Davis et al. 1985).
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